We show that sensitive thermal detectors should be useful for measuring very small energy pulses, such as those produced by the absorption of xhyphen;ray photons. The measurement uncertainty can be very small, making the technique promising for high resolution nondispersive xhyphen;ray spectroscopy. We derive the limits to the energy resolution of such thermal detectors. We use these to find the resolution to be expected for a detector suitable for xhyphen;ray spectroscopy in the 100ndash;10thinsp;000 eV range. If there is no noise in the thermalization of the xhyphen;ray, resolution better than 1 eV full width at half maximum (FWHM) is possible for detectors operating at 0.1 K. Energy loss in the conversion of the photon energy to heat is a potential problem. Statistical fluctuations of lost energy would reduce the energy resolution of the detector. The loss mechanisms may include emission of photons or electrons, or the trapping of energy in longhyphen;lived metastable states. Fluctuations in the phonon spectrum could also limit the resolution if phonon relaxation times are very long. We give conceptual solutions for each of these possible problems.
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